8. -12 points SerPSET9 30.P067. My Notes Ask Your Teacher Fifty-three turns of i

Question

8. -12 points SerPSET9 30.P067. My Notes Ask Your Teacher Fifty-three turns of insulated wire 0.100 cm in diameter are tightly wound to form a flat spiral. The spiral fills a disk surrounding a cirdle of radius 5.00 cm and extending to a radius 10.30 cm at the outer edge. Assume the wire carries a current I at the center of its cross section. Approximate each turn of wire as a circle. Then a loop of current exists at radius 5.05 cm, another at 5.15 cm, and so on. Numerically calculate the magnetic field at the center of the coil. (Assume B is in teslas and I is in amperes.) Need Help? Read

Explanation / Answer

Each turn creates a field at the center

B=uoI/2R

Therefore total magnetic field is

B=(uoI/2)[1/R1 +1/R2 +1/R3+------+1/R53]

B=((4pi*10-7)*I/2)[1/5.05 +1/5.15 +1/5.25+1/5.35+1/5.45+--------+1/10.15+1/10.25]*102

B=(2pi*10-7)I*(7.227)*102

B=(4.54*10-4)I

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